# Chapter 10 gases lecture outline

W
Shared by:
Categories
Tags
-
Stats
views:
1
posted:
8/8/2012
language:
simple
pages:
6
Document Sample

Chapter 10. Gases

10.1 Characteristics of Gases
•       All substances have three phases: solid, liquid and gas.
•       Substances that are liquids or solids under ordinary conditions may also exist as gases.
•        These are often referred to as vapors.
•       Many of the properties of gases differ from those of solids and liquids:
•        Gases are highly compressible and occupy the full volume of their containers.
•        When a gas is subjected to pressure, its volume decreases.
•        Gases always form homogeneous mixtures with other gases.
•       Gases only occupy a small fraction of the total volume of their containers.
•        As a result, each molecule of gas behaves largely as though other molecules were absent.

10.2 Pressure
•       Pressure is the force acting on an object per unit area:

F
P
A
Atmospheric Pressure and the Barometer
•      The SI unit of force is the newton (N).
•        1 N = 1 kgm/s2
•      The SI unit of pressure is the pascal (Pa).
•        1 Pa = 1 N/m2
•        A related unit is the bar, which is equal to 105 Pa.
•      Gravity exerts a force on the Earth’s atmosphere.
•        A column of air 1 m2 in cross section extending to the upper atmosphere exerts a force of
5
10 N.
•        Thus, the pressure of a 1 m2 column of air extending to the upper atmosphere is 100 kPa.
•         Atmospheric pressure at sea level is about 100 kPa or 1 bar.
•        The actual atmospheric pressure at a specific location depends
on the altitude and the weather conditions.
•      Atmospheric pressure is measured with a barometer.
•        If a tube is completely filled with mercury and then inverted into a container of mercury
open to the atmosphere, the mercury will rise 760 mm up the tube.
•        Standard atmospheric pressure is the pressure required to support 760 mm of Hg in a
column.
•        Important non SI units used to express gas pressure include:
•         atmospheres (atm)
•         millimeters of mercury (mm Hg) or torr
•         1 atm = 760 mm Hg = 760 torr = 1.01325 x 105 Pa = 101.325 kPa

10.3 The Gas Laws
•   The equations that express the relationships among T (temperature), P (pressure), V (volume), and n
(number of moles of gas) are known as the gas laws.
The Pressure-Volume Relationship: Boyle’s Law
•   Weather balloons are used as a practical application of the relationship between pressure and volume
of a gas.
•        As the weather balloon ascends, the volume increases.
•        As the weather balloon gets further from Earth’s surface, the atmospheric pressure
decreases.
• Boyle’s law: The volume of a fixed quantity of gas, at constant temperature, is inversely proportional
to its pressure.
•       Mathematically:
1
V  constan 
t        or PV  constant
P
•        A plot of V versus P is a hyperbola.

V
V  constant T or           constant
T
•         A plot of V versus 1/P must be a straight line passing through the origin.
•       The working of the lungs illustrates that:
•         as we breathe in, the diaphragm moves down, and the ribs expand; therefore, the volume
of the lungs increases.
•         according to Boyle’s law, when the volume of the lungs increases, the pressure decreases;
therefore, the pressure inside the lungs is less than the atmospheric pressure.
•         atmospheric pressure forces air into the lungs until the pressure once again equals
atmospheric pressure.
•         as we breathe out, the diaphragm moves up and the ribs contract; therefore, the volume of
the lungs decreases.
•         By Boyle’s law, the pressure increases and air is forced out.
The Temperature-Volume Relationship: Charles’s Law
•        We know that hot-air balloons expand when they are heated.
• Charles’s law: The volume of a fixed quantity of gas at constant pressure is directly proportional to its
absolute temperature.
•        Mathematically:
•        Note that the value of the constant depends on the pressure and the number of moles of
gas.
•        A plot of V versus T is a straight line.
•        When T is measured in C, the intercept on the temperature axis is –273.15C.
•        We define absolute zero, 0 K = –273.15C.
• Gay-Lussac’s law of combining volumes: At a given temperature and pressure the volumes of gases
that react with one another are ratios of small whole numbers.
• Avogadro’s hypothesis: Equal volumes of gases at the same temperature and pressure contain the
same number of molecules.
• Avogadro’s law: The volume of gas at a given temperature and pressure is directly proportional to the
number of moles of gas.
•        Mathematically:
V = constant x n
•       We can show that 22.4 L of any gas at 0C and 1 atmosphere contains 6.02 x 1023 gas
molecules.

10.4 The Ideal-Gas Equation
•       Summarizing the gas laws:
•         Boyle: V  1/P (constant n, T)
•         Charles: V  T (constant n, P)
•         Avogadro:         V  n (constant P, T)
•         Combined:         V  nT/P
•       Ideal gas equation: PV = nRT
•         An ideal gas is a hypothetical gas whose P, V, and T behavior is completely described by
the ideal-gas equation.
•         R = gas constant = 0.08206 Latm/molK
•        Other numerical values of R in various units are given in Table 10.2.
•       Define STP (standard temperature and pressure) = 0C, 273.15 K, 1 atm.
•        The molar volume of 1 mol of an ideal gas at STP is 22.41 L.
Relating the Ideal-Gas Equation and the Gas Laws
•       If PV = nRT and n and T are constant, then PV is constant and we have Boyle’s law.
•        Other laws can be generated similarly.
• In general, if we have a gas under two sets of conditions, then
PV1 P2V2
1

n1T1 n2T2

•   We often have a situation in which P, V, and T all change for a fixed number of moles of gas.
• For this set of circumstances,

PV
 nR  constant
T
•    Which gives

P1V1 P2V2

T1   T2

10.5 Further Applications of the Ideal-Gas Equation
Gas Densities and Molar Mass
•      Density has units of mass over volume.
•      Rearranging the ideal-gas equation with M as molar mass we get

n   P

V RT
nM PM

V   RT
PM
d 
RT
•       The molar mass of a gas can be determined as follows:
dRT
M
P

Volumes of Gases in Chemical Reactions
•       The ideal-gas equation relates P, V, and T to number of moles of gas.
•       The n can then be used in stoichiometric calculations.

10.6 Gas Mixtures and Partial Pressures
•       Since gas molecules are so far apart, we can assume that they behave independently.
•       Dalton observed:
•         The total pressure of a mixture of gases equals the sum of the pressures that each
would exert if present alone.
•         Partial pressure is the pressure exerted by a particular component of a gas mixture.
• Dalton’s law of partial pressures: In a gas mixture the total pressure is given by the sum of partial
pressures of each component:
Pt = P1 + P2 + P3 + …
•       Each gas obeys the ideal gas equation.
•        Thus,
RT      RT
Pt  (n1  n2  n3  )       nt
V       V
Partial Pressures and Mole Fractions
•        Let n be the number of moles of gas 1 exerting a partial pressure P1, then
1
P1 = Pt
•        where  is the mole fraction (n1/nt).
•        Note that a mole fraction is a dimensionless number.
Collecting Gases over Water1
•        It is common to synthesize gases and collect them by displacing a volume of water.
•        To calculate the amount of gas produced, we need to correct for the partial pressure of the water:
Ptotal = Pgas + Pwater
• The vapor pressure of water varies with temperature.
•        Values can be found in Appendix B.

10.7 Kinetic-Molecular Theory
•       The kinetic-molecular theory was developed to explain gas behavior.
•        It is a theory of moving molecules.
•       Summary:
•        Gases consist of a large number of molecules in constant random motion.
• The combined volume of all the molecules is negligible compared with the volume of the
container.
•        Intermolecular forces (forces between gas molecules) are negligible.
•        Energy can be transferred between molecules during collisions, but the average kinetic
energy is constant at constant temperature.
•        The collisions are perfectly elastic.
•        The average kinetic energy of the gas molecules is proportional to the absolute
temperature.
•       Kinetic molecular theory gives us an understanding of pressure and temperature on the molecular
level.
•        The pressure of a gas results from the collisions with the walls of the container.
•        The magnitude of the pressure is determined by how often and how hard the molecules
strike.
•       The absolute temperature of a gas is a measure of the average kinetic energy.
•              Some molecules will have less kinetic energy or more kinetic energy than the
average
(distribution).
•        There is a spread of individual energies of gas molecules in any sample of gas.
•        As the temperature increases, the average kinetic energy of the gas molecules increases.
•       As kinetic energy increases, the velocity of the gas molecules increases.
•        Root-mean-square (rms) speed, u, is the speed of a gas molecule having average kinetic
energy.
•       Average kinetic energy, , is related to rms speed:
 = ½mu2
•          where m = mass of the molecule.
Application to the Gas-Laws
• We can understand empirical observations of gas properties within the framework of the kinetic-
molecular theory.
•       The effect of an increase in volume (at constant temperature) is as follows:
•        As volume increases at constant temperature, the average kinetic energy of the gas
remains constant.
•        Therefore, u is constant.
•        However, volume increases, so the gas molecules have to travel further to hit the walls of
the container.
•        Therefore, pressure decreases.
•       The effect of an increase in temperature (at constant volume) is as follows:
•        If temperature increases at constant volume, the average kinetic energy of the gas
molecules increases.
•        There are more collisions with the container walls.
•        Therefore, u increases.
•        The change in momentum in each collision increases (molecules strike harder).
•        Therefore, pressure increases.

10.8 Molecular Effusion and Diffusion
•        The average kinetic energy of a gas is related to its mass:
 = ½m 2
•   Consider two gases at the same temperature: the lighter gas has a higher rms speed than the heavier
gas.
•       Mathematically:
3RT
u
M
•      The lower the molar mass, M, the higher the rms speed for that gas at a constant
temperature.
•       Two consequences of the dependence of molecular speeds on mass are:
•      Effusion is the escape of gas molecules through a tiny hole into an evacuated space.
•      Diffusion is the spread of one substance throughout a space or throughout a second
substance.

Graham’s Law of Effusion
•   The rate of effusion can be quantified.
•       Consider two gases with molar masses, M1 and M2, and with effusion rates, r1 and r2, respectively.
•       The relative rate of effusion is given by Graham’s law:
r1       M2

r2       M1
•       Only those molecules which hit the small hole will escape through it.
•        Therefore, the higher the rms speed the more likely it is that a gas molecule will hit the
hole.
•        We can show
r1 u1          M2
    
r2 u 2         M1
Diffusion and Mean Free Path
•       Diffusion is faster for light gas molecules.
•       Diffusion is significantly slower than the rms speed.
•        Diffusion is slowed by collisions of gas molecules with one another.
•        Consider someone opening a perfume bottle: It takes awhile to detect the odor, but the
average speed of the molecules at 25C is about 515 m/s (1150 mi/hr).
•       The average distance traveled by a gas molecule between collisions is called the mean free path.
•       At sea level, the mean free path for air molecules is about 6 x 10 – 6 cm.

10.9 Real Gases: Deviations from Ideal Behavior
•       From the ideal gas equation:
PV
n
RT
•        For 1 mol of an ideal gas, PV/RT = 1 for all pressures.
•        In a real gas, PV/RT varies from 1 significantly.
•        The higher the pressure the more the deviation from ideal behavior.
•        For 1 mol of an ideal gas, PV/RT = 1 for all temperatures.
•        As temperature increases, the gases behave more ideally.
•       The assumptions in the kinetic-molecular theory show where ideal gas behavior breaks down:
•        The molecules of a gas have finite volume.
•        Molecules of a gas do attract each other.
•       As the pressure on a gas increases, the molecules are forced closer together.
•        As the molecules get closer together, the free space in which the molecules can move gets
smaller.
•        The smaller the container, the more of the total space the gas molecules occupy.
•        Therefore, the higher the pressure, the less the gas resembles an ideal gas.
•        As the gas molecules get closer together, the intermolecular distances decrease.
•        The smaller the distance between gas molecules, the more likely that attractive forces will
develop between the molecules.
•        Therefore, the less the gas resembles an ideal gas.
•       As temperature increases, the gas molecules move faster and further apart.
•        Also, higher temperatures mean more energy is available to break intermolecular forces.
•        As temperature increases, the negative departure from ideal-gas behavior disappears.

The van der Waals Equation
•   We add two terms to the ideal gas equation to correct for
•       the volume of          V  nb  molecules:
•        for molecular attractions:
 n2a 
 2 
V 
     
•        The correction terms generate the van der Waals equation:
•        where a and b are empirical constants that differ for each gas.
    n2a 
 P  2 V  nb  nRT
    V 
        
•         van der Waals constants for some common gases can be found in Table 10.3.
•   To understand the effect of intermolecular forces on pressure, consider a molecule that is about to
strike the wall of the container.
•        The striking molecule is attracted by neighboring molecules.
•        Therefore, the impact on the wall is lessened.

Related docs
Other docs by HC120808144835
lord of the flies chapter 10 worksheet